The right answer is Option 2: A right triangle with side length of √47 and hypotenuse of 10.
Step-by-step explanation:
We know that;
![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
We will put the unknown length as √53 to check the solution.
Option 1: a = 6 , b = √53 , c = √91
![(6)^2+(\sqrt{53})^2=(\sqrt{91})^2\\36+53=91\\89\neq 91](https://tex.z-dn.net/?f=%286%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%28%5Csqrt%7B91%7D%29%5E2%5C%5C36%2B53%3D91%5C%5C89%5Cneq%2091)
Option 2: a=√47, b = √53, c = 10
![(\sqrt{47})^2+(\sqrt{53})^2=(10)^2\\47+53=100\\100=100](https://tex.z-dn.net/?f=%28%5Csqrt%7B47%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%2810%29%5E2%5C%5C47%2B53%3D100%5C%5C100%3D100)
Option 3: a = √19, b=√53, c= √34
![(\sqrt{19})^2+(\sqrt{53})^2=(\sqrt{34})^2\\19+53=34\\72\neq 34](https://tex.z-dn.net/?f=%28%5Csqrt%7B19%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%28%5Csqrt%7B34%7D%29%5E2%5C%5C19%2B53%3D34%5C%5C72%5Cneq%2034)
Option 4: a=√73, b=√53, c=20
![(\sqrt{73})^2+(\sqrt{53})^2=(20)^2\\73+53=400\\126\neq 400](https://tex.z-dn.net/?f=%28%5Csqrt%7B73%7D%29%5E2%2B%28%5Csqrt%7B53%7D%29%5E2%3D%2820%29%5E2%5C%5C73%2B53%3D400%5C%5C126%5Cneq%20400)
Option 2 satisfies pythagoras theorem.
Therefore;
The right answer is Option 2: A right triangle with side length of √47 and hypotenuse of 10.
Keywords: pythagoras theorem, square root
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